Analysis for Understanding PDEs in Introduction & Farlow Books

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In summary: While these topics may seem complex, they are critical to understanding and solving PDE's. Both textbooks being used in this class will cover these topics in depth.
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romsofia
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Hey there, today my prof. said the next two lectures will be completely devoted to analysis in order to understand the PDE's we will be working with (We already derived the heat eq'n). We started off with sets today, not to bad; however, I was wondering how deep will we be going into analysis in order to understand the PDE's, so I could look up stuff (Seems like I'm the only student in the class without a heavy analysis background :X)?

We are using the book "Introduction to Partial Differential Equations with Applications by E. C. Zachmanoglou and Dale Thoe" and "Partial Differential Equations for Scientists and Engineers by Stanley Farlow".

Thanks for any help!
 
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Since we cannot see your profs lesson plans there is no way to answer. Ask your prof.
 
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romsofia said:
Hey there, today my prof. said the next two lectures will be completely devoted to analysis in order to understand the PDE's we will be working with (We already derived the heat eq'n). We started off with sets today, not to bad; however, I was wondering how deep will we be going into analysis in order to understand the PDE's, so I could look up stuff (Seems like I'm the only student in the class without a heavy analysis background :X)?

We are using the book "Introduction to Partial Differential Equations with Applications by E. C. Zachmanoglou and Dale Thoe" and "Partial Differential Equations for Scientists and Engineers by Stanley Farlow".

Thanks for any help!

Most of the real and complex analysis in PDE's is related to the Fourier Series, derivation of the Fourier Integrals, Dirichlet Kernel, Parseval's theroem, convergence and divergence of the sereis:

http://en.wikipedia.org/wiki/Fourier_series
 

FAQ: Analysis for Understanding PDEs in Introduction & Farlow Books

What is the purpose of analysis in understanding PDEs?

The purpose of analysis in understanding PDEs is to use mathematical tools and techniques to study the properties and behavior of solutions to partial differential equations. This allows us to gain a deeper understanding of the underlying physical phenomena and make predictions about the system being modeled.

What are some common techniques used in PDE analysis?

Some common techniques used in PDE analysis include separation of variables, Fourier series, Laplace transforms, and Green's functions. These methods help us to solve PDEs and analyze their solutions.

3. How does the Introduction to PDEs book differ from the Farlow PDE book?

The Introduction to PDEs book provides a general overview of the theory and applications of PDEs, while the Farlow PDE book focuses on specific techniques and examples. The Introduction book may be more suitable for beginners, while the Farlow book may be more useful for those with a stronger mathematical background.

4. Are there any real-world applications of PDE analysis?

Yes, PDE analysis has many important real-world applications in fields such as physics, engineering, finance, and biology. For example, PDEs are commonly used to model heat transfer, fluid dynamics, and option pricing in financial markets.

5. Is it necessary to have a strong background in mathematics to understand PDE analysis?

While a strong background in mathematics is certainly helpful, it is not always necessary to understand PDE analysis. Both the Introduction to PDEs and Farlow PDE books provide a step-by-step approach to learning PDE analysis, making it accessible to a wide range of readers. However, a basic understanding of calculus and linear algebra is recommended.

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